Prospect Theoretic Approach to Pursuit-evasion Differential Games with Risk Aversion and Probability Sensitivity

This paper considers pursuit-evasion (PE) differential games in which the pursuer's and evader's irrational perceptions of environmental uncertainty lead to deviations from rational controllers. Firstly, the equivalent irrational behavioral models of risk aversion and probability sensitivity are established using Cumulative Prospect Theory (CPT). Secondly, sufficient conditions for capturability are established in terms of irrationality parameters. Finally, the CPT-Nash equilibrium is analyzed by Brouwer's fixed-point and self-consistency theorem. The new results reveal that irrational behaviors benefit the pursuer in some cases and the evader in others. Certain captures that are unachievable under rational behaviors can be achieved under irrational ones. By bridging irrational behavior with game-based control, a theoretical foundation is established for human-machine control systems.